A collocated isogeometric finite element method based on Gauss–Lobatto Lagrange extraction of splines

• Published in: Computer methods in applied mechanics and engineering Vol. 316; pp. 720 - 740
• Main Authors: Nguyen, Lam H., Schillinger, Dominik
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2017; Elsevier BV
• Subjects: Collocation; Collocation methods; Finite element analysis; Finite element method; Galerkin method; Gauss–Lobatto Lagrange extraction; Geometry; Isogeometric analysis; Lagrange multiplier; Splines; Studies; Isogeometric analysis; Collocation; Gauss–Lobatto Lagrange extraction
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.09.036

Generalizing the concept of Bézier extraction, we introduce an extraction operator that links C0 Gauss–Lobatto Lagrange functions with smooth splines. This opens the door for collocated isogeometric analysis that combines the accuracy of the Galerkin method with collocation-type formation and assembly procedures. We present the key ingredients of the technology, i.e. integration by parts and the weighted residual form, the interaction of Gauss–Lobatto Lagrange extraction with Gauss–Lobatto quadrature, and symmetrization with the ultra-weak formulation. We compare the new method with standard isogeometric Galerkin and isogeometric point-collocation methods for spline discretizations in three dimensions. •We introduce an extraction operator that links Gauss–Lobatto Lagrange (GLL) functions with splines.•Collocated IGA is based on the weighted residual form, Gauss–Lobatto quadrature, and GLL extraction.•We compare collocated IGA with isogeometric Galerkin and point-collocation.